List of top Mathematics Questions

If $x = a + b, y = a \omega +b \omega ^2$ and $z = a \omega^2 + b \omega$, then which one of the following is true.

If $b$ and $c$ are odd integers, then the equation $x^2 + bx + c = 0$ has

The principal value of the $arg (z)$ and $ | z |$ of the complex number $z=1+\cos\left(\frac{11\pi}{9}\right)+ i \, \sin\frac{11\pi}{9}$ are respectively

$\left(\frac{1}{1-2i} + \frac{3}{1+i}\right) \left(\frac{3+4i}{2-4i}\right)$ is equal to :

If $P$ is the affix of $z$ in the Argand diagram and $P$ moves so that $\frac{z-i}{z-1}$ is always purely imaginary, then locus of $z$ is

The value of $ \begin{vmatrix} b+c&a&a\\ b &c+a &b\\ c & c &a+b \end{vmatrix}$ is

If the three linear equations $x + 4ay + az = 0$ $x + 3 by + bz = 0$ and $x + 2cy + cz = 0$ have a non-trivial solution, then a, b, c are in

The matrix 'X' in the equation $AX = B$, such that $A = \begin{bmatrix}1&3\\ 0&1\end{bmatrix}$ and $ B = \begin{bmatrix}1&-1\\ 0&1\end{bmatrix}$ is given by

The only integral root of the equation $ \begin{vmatrix} 2-y &2&3\\ 2 &5-y &6\\ 3 & 4 & 10-y \end{vmatrix}$=0 is

$B$ is an extremity of the minor axis of an ellipse whose foci are $S$ and $S'$. If $?SBS'$ is a right angle, then the eccentricity of the ellipse is

Which of the following functions are one-one and onto ?

The value of $ \frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ } $ is equal to

Let $S(n)$ denote the sum of the digits of a positive integer n. e.g. $S(178)=1+$ $7+8=16 .$ Then, the value of $S(1)+S(2)+S(3)+\ldots+S(99)$ is

$ \int{(x+1){{(x+2)}^{7}}}(x+3)dx $ is equal to

$ \int{\frac{\sec x cosec x}{2\cot x-\sec x\cos ecx}}dx $ is equal to

$ \int{\frac{{{4}^{x+1}}-{{7}^{x-1}}}{{{28}^{x}}}}dx $ is equal to

$ \int{\frac{\cos x-\sin x}{1+2\sin x\cos x}}dx $ is equal to

The vectors of magnitude $a, 2a, 3a $ meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is

If a straight line makes angles $\alpha , \beta , \gamma $ with the coordinate axes, then $\frac{1-\tan^{2} \alpha }{1+tan^{2} \alpha} +\frac{1}{sec 2 \beta} -2\sin^{2} \gamma =$

If the produce of five consecutive terms of a $G.P.$ is $\frac{243}{32}$ , then the middle term is

If the roots of the quadratic equation $mx^2 - nx + k = 0$ are tan $33^{\circ}$ and $\tan\, 12^{\circ}$ then the value of $\frac{2m+n+k}{m}$ is equal to

If $ \frac{5{{z}_{2}}}{11{{z}_{1}}} $ is purely imaginary, then the value of $ \left[ \frac{2{{z}_{1}}+3{{z}_{2}}}{2{{z}_{1}}-3{{z}_{2}}} \right] $ is

$\displaystyle \lim_{x \to 0} $ $\frac{\left(1+2x\right)^{10}-1}{x}$ is equal to

Let $p, q, r$ be three statements. Then $\sim (p \vee \left(q \wedge r\right))$ is equal to